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Fuzzy Clustering

What Is Data Clustering?

Clustering of numerical data forms the basis of many classification
and system modeling algorithms. The purpose of clustering is to identify natural groupings of data from
a large data set to produce a concise representation of a system's
behavior.

Fuzzy Logic Toolbox™ tools allow you to find clusters in input-output
training data. You can use the cluster information to generate a Sugeno-type
fuzzy inference system that best models the data behavior using a
minimum number of rules. The rules partition themselves according
to the fuzzy qualities associated with each of the data clusters.
Use genfis2 or genfis3 to
automatically accomplish this type of FIS generation.

Fuzzy C-Means Clustering

Fuzzy c-means (FCM) is a data clustering
technique wherein each data point belongs to a cluster to some degree
that is specified by a membership grade. This technique was originally
introduced by Jim Bezdek in 1981 [1] as
an improvement on earlier clustering methods. It provides a method
that shows how to group data points that populate some multidimensional
space into a specific number of different clusters.

The command line function fcm starts
with an initial guess for the cluster centers, which are intended
to mark the mean location of each cluster. The initial guess for these
cluster centers is most likely incorrect. Additionally, fcm assigns
every data point a membership grade for each cluster. By iteratively
updating the cluster centers and the membership grades for each data
point, fcm iteratively moves the cluster centers
to the right location within a data set. This iteration is based on
minimizing an objective function that represents the distance from
any given data point to a cluster center weighted by that data point's
membership grade.

The command line function fcm outputs a
list of cluster centers and several membership grades for each data
point. You can use the information returned by fcm to
help you build a fuzzy inference system by creating membership functions
to represent the fuzzy qualities of each cluster.

The genfis3 function uses fcm to
take input-output training data and generate a Sugeno-type fuzzy inference
system that models the data behavior.

Subtractive Clustering

If you do not have a clear idea how many clusters there should
be for a given set of data, subtractive clustering is
a fast, one-pass algorithm for estimating the number of clusters and
the cluster centers for a set of data [2]. The cluster estimates, which are obtained from the subclust function, can be used to initialize
iterative optimization-based clustering methods (fcm)
and model identification methods (likeanfis).
The subclust function finds the clusters by using
the subtractive clustering method.

The genfis2 function builds
upon the subclust function to provide a fast,
one-pass method to take input-output training data and generate a Sugeno-type fuzzy inference system
that models the data behavior.